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Award ID contains: 1949820

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  1. ; (, Journal of the European Mathematical Society)
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  2. ; (, Probability Theory and Related Fields)
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  3. ; ; (, Communications in Mathematical Physics)
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  4. ; (, The Annals of Statistics)
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  5. ; ; (, The Annals of Applied Probability)
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  6. ; ; (, Proceedings of the London Mathematical Society)
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  7. ; (, American Journal of Mathematics)
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  8. ; ; (, International Mathematics Research Notices)
    null (Ed.)
    Abstract We introduce and study a new family of $$q$$-translation-invariant determinantal point processes on the two-sided $$q$$-lattice. We prove that these processes are limits of the $$q$$–$zw$ measures, which arise in the $$q$$-deformation of harmonic analysis on $$U(\infty )$$, and express their correlation kernels in terms of Jacobi theta functions. As an application, we show that the $$q$$–$zw$ measures are diffuse. Our results also hint at a link between the two-sided $$q$$-lattice and rows/columns of Young diagrams. 
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